Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 22}$ ${5x-2y = -15}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $7x = 7$ $\dfrac{7x}{{7}} = \dfrac{7}{{7}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x+2y = 22}\thinspace$ to find $y$ ${2}{(1)}{ + 2y = 22}$ $2+2y = 22$ $2{-2} + 2y = 22{-2}$ $2y = 20$ $\dfrac{2y}{{2}} = \dfrac{20}{{2}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {5x-2y = -15}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ - 2y = -15}$ ${y = 10}$